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NCERT Solution Class 6 Maths Chapter -3 Playing With Numbers


NCERT Solution Class 6 Maths Chapter -3 Playing With Numbers

Exercise 1


1. Find the sum of any two numbers ?
(a) odd numbers
(b) even numbers
Solution (a)
e.g. 6 + 3 = 9
Solution(b)
e.g. 12 + 14 = 26


2. Write down the prime numbers less than 20.
Solution:  The numbers which are divisible by itself is known as prime numbers . prime numbers which are less than 20 are    2 , 3 , 5 , 7 , 11 , 13 , 17 , 19


3. Write down the composite numbers less than 20.

Solution: The numbers which are not prime numbers is known as composite numbers. The composite numbers which are less than 20 are 4 , 6 , 8 , 9 , 10 , 12 , 14 , 15 , 16 , 18 .


5. Express the following in the form of sum of two odd primes.
solution :
(a) 24 = 5 + 19
(b) 44 = 7 + 37
(c) 18 = 7 + 11
(d) 36 = 31 + 5


6. Find any three pair of prime numbers whose difference is two.
solution :
Two prime numbers whose difference is ‘2’ is also called as twin primes or twin prime number.
3 pairs : (41 , 43) ( 73 , 71) (5 , 3)


7. Express the following numbers in the form of sum of three odd primes.
solution :
(a) 53 = 31 + 3 + 19
(b) 61 = 19 + 11 + 31
(c) 31 = 19 + 5 + 7


8. Write down the 3 pairs of prime numbers which is less than 20 and also whose sum is divisible by 5.

solution :
(*) 17 + 3 = 20 (5 x 4 = 20. It is divisible by 5)
(*) 13 + 2 = 15 (5 x 3 = 15. It is divisible by 5)
(*) 11 + 19 = 30 ( 5 x 6 = 30. It is divisible by 5)


9. FILL IN THE BLANKS.
(*) 1 is neither _____ nor ________. ans:     (composite , prime)
(*) The number which has only one factor is called _________. ans:    (prime number)
(*) The smallest composite number is ________. ans:  ( 4 )


10. TRUE OR FALSE.
(*) The sum of two prime numbers is always even.       Ans : false
e.g. 3 + 2 = 5 (i.e) odd
(*) The product of three odd numbers is odd.                Ans : true
e.g. 5 x 7 x 3 = 105 (i.e) odd
(*) The product of two even numbers is always even.   Ans : true
e.g 2 x 4 = 8 (i.e) even
6 x 2 = 12 (i.e) even


Exercise 2


1. Find out the common factors of the following.
(a) 28 & 20
(b) 25 & 15
(c) 56 & 120

solution :
(a) Factors of (20) = 1 , 10 , 20, 2 , 4 ,5
Factors of (28) = 7 , 14 , 28 ,1 , 2 , 4 ,
The factors that are common are : 4, 2, 1
(b) Factors of (15) = 1 , 15,3 , 5
Factors of (25) = 1 ,25,5
The factors that are common are : 1 , 5.
(c) Factors of (56) = 1 , 14 , 28 , 56 ,2 , 4 , 7 , 8.
Factors of (120) = 1 ,30 ,40 , 10 ,12 , 2 ,3 ,4 ,5 ,6 ,8 , 15 ,20 ,24 ,60 , 120.
The factors that are common are : 1 , 2 , 4 , 8 .


2. Find the numbers (all) which are less than 100 and also common multiples of 4 & 3.
solution :
(*) multiples of 3 = 3, 15, , 6, 9, 12
(*) multiples of 4 = 4 ,8, 12, 16, 20
The Common multiples are = 12, 36, 48,24, 60, 72, 84, 96.


3. From the given numbers , find which numbers are co prime numbers ?
(a) 68 and 17
(b) 16 and 81
(c) 35 and 18
solution :
(*) 68 and 17
Factors of 68 = 1, 2, 4, 17, 34, 68
Factors of 17 = 1, 17
The factors that are common are : 1 , 17
Since it has common factors other than 1, the above given 2 number is not a co prime.
(*) 16 and 81
Factors of 16 = 1, 2, 4, 8, 16
Factors of 81 = 1, 3, 9, 27, 81
The common factor is 1. Therefore the given two number is co prime.
(*) 35 and 18
Factors of 35 = 1, 5, 7, 35
Factors of 18 = 1, 2, 3, 6, 9, 18
Common factor is 1. Therefore the given two number is co prime.


4. A particular number is divisible by both 14 and 5. Find the other number that is always divisible.
solution :

Factors of 5 = 1 , 5
Factors of 14 = 1, 2, 7
The common factors of these numbers is 1. Therefore, the given two number is co prime number and also the number will be divisible by their product.


5. A number is divisible by 12. Find the other numbers, which are divisible of 12.
solution :
The factors are : 1, 2, 3, 4, 6 , 12
Therefore, the numbers 1,2,3,4,6 other than 12 by which this number is also divisible.


6. Find the common factors of the following given below:
(*) 4 , 8 and 12
(*) 5 , 15 , 25
solution :
(*) 4 , 8 and 12
Factors of 4 = 1 , 2 , 4
Factors of 8 = 1 , 2 , 4 , 8
Factors of 12 = 1 , 2 , 3 , 4 , 6 , 12
The common factors are : 1, 2, 4.
(*) 5 , 15 , 25
The factors of 5 = 1 , 5
The factors of 15 = 1 , 3 , 5 , 15
The factors of 25 = 1 , 5 , 25
The common factors are : 1 , 5


 

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